The Black Swan vs. Power Law

Much talk this year about Nicholas Taleb’s Black Swan. (For short and long — but remarkably lucid — discussions of the concept, from a completely non-mathematical perspective, take a look at this excellent introduction from Grumpy Old Bookman.)

Most of the coverage of the concept has been laudatory, so it’s useful to hear a discouraging word, especially from the great thinker Stewart Brand.

Like most readers, I expect, I know Brand for his incredible outpouring of new ideas — about ways to live, to see, about how buildings learn, on and on beyong recounting except on Wikipedia.

So it’s actually refreshing to hear Brand sounding a little grumpy about Black Swans, in Edge:

Taleb seems oddly innocent of "power law" behavior, in which Black Swans hold a much different position than "outlier," "tail," etc. — all Bell Curve denotations, in power law phenomena, nothing is far from typical, because nothing whatever is typical.

The violence/incident of terrorist incidents can be charted on a power law curve, not a Bell curve.

At base, this criticism is indisputable: a Black Swan is nothing but an extreme example of a familiar phenomenon, the impact of the improbable. You cannot predict a 9/11 or Katrina with a Bell curve.

But it helps us put it in a context. Power laws are nothing new, if not easy to remember. Numerous named examples exist. The Black Swan is a point on a distribution itself. Mustn’t leap to the assumption that the highly improbable must be bad…it’s not necessarily the case. (Taleb would agree, but that’s not why his book is being read around the world.) The graph in Wikipedia makes the point wonderfully clear by charting not a horror but a delight. Popularity.

To wit:

"An example power law graph, being used to demonstrate ranking of
popularity. To the right is the long tail, to the left are the few that
dominate (also known as the 80-20 rule)."

300pxlong_tail

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